Evaluate Where F(x, Y, Z) = -X I - $\sigma$

question 90

Essay

Evaluate where F(x, y, z) = -x i - 2x j + (z - 1)k and $\sigma$ is the surface enclosed by that portion of the paraboloid z = 4 - y² which lies in the first octant and is bounded by the coordinate planes and the plane y = x. The surface is oriented by upward unit normals.

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Definitions:

Test Statistic

A calculated value used in statistical testing to determine whether to reject the null hypothesis.

P-Value

The probability of observing test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct.

Degrees of Freedom

The number of independent values or quantities that can vary in the calculation without violating any constraint.

Contingency Table

A tabular method used to summarize the relationship between several categorical variables, showing distribution of frequencies.